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Perform a one-sided hypothesis t-test

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I need some help with the following assignment:

In an attempt to determine whether or not special training increases the speed with which assembly line workers can do an assembly job at AMTEL Inc., 25 workers are timed performing the task. Then, they are given a special training course designed to increases their assembly efficiency. At the end of the course, they are timed doing the same task. The differences between the first and the second time are recorded for each of the 25 assembly line workers. The mean improvement for the 25 workers was found to be 2.5 minutes and the sample standard deviation was 4 minutes.

Let variable X represents the improvement in time for each assembly line worker. Let ? represents the average improvement in time for the population. Has the training improved the time required on the job? Please test the hypothesis use ?=0.05 as the level of significance

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The solution consists of a standard five-step one-sided hypothesis t-test for the population mean.

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5 Step Hypothesis Test

The following data represents the running time of films produced by 2 motion picture companies. Assume these are independent samples

Company Time (in minutes)
Company 1 102 86 98 109 92
Company 2 81 165 97 134 92 87 114

Test the null hypothesis that the average running time of the films produced by company 2 exceeds the average running time of films produced by company 1 by an amount of 10 minutes. Test against the null hypothesis of a one sided alternative that the difference is more than 10 minutes. Use a .1 level of significance (alpha).

a) Perform the Hypothesis test at alpha = 0.10
b) Determine the confidence interval for the difference between the means at 90% CI

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